Question

A group of boys and girls is in a room. 5 girls leave the room, and the remaining group is in a ratio of boys to girls that is equal to 3:2. After this, 12 boys leave the room, and the remaining group is in a ratio of boys to girls that is equal to 3:4. Before all the departures, how many boys and how many girls were in the room?

Answer 1

Let the number of boys = x

Let the number of girls = y

5 girls leave

x /( y-5) = 3/2

2x = 3y - 15

2x - 3y = -15 ------ (1)


12 boys leave

(x -12)/(y - 5) = 3/4

4x -  3y = 33  ----------- (ii)


Subtract (i) from (ii)

2x  = 48

x = 24


2x - 3y = -15

2(24) - 3y = -5

48 - 3y = -15

-3y = -63

y = 21


The number of boys was 24

The number of girls was 21

Answer 2

Answer:

Step-by-step explanation:

Let the number of boys = x

Let the number of girls = y

5 girls leave

x /( y-5) = 3/2

2x = 3y - 15

2x - 3y = -15 ------ (1)

12 boys leave

(x -12)/(y - 5) = 3/4

4x - 3y = 33 ----------- (ii)

Subtract (i) from (ii)

2x = 48

x = 24

2x - 3y = -15

2(24) - 3y = -5

48 - 3y = -15

-3y = -63

y = 21

The number of boys was 24

The number of girls was 21